i-96 case study: jointed concrete pavement curling and warp … byrum.pdf · 2020-04-17 · rwp. 30...

30 years on the Road To Progressively Better Data

I-96 Case Study: Jointed Concrete Pavement Curling and Warp Presented in the Context of

Pavement Asset ManagementChristopher R. Byrum, PhD, PE


M EI d zdx

=2

2

M Eh zxx = −

3

2

2

212 1( )µ∂∂

3-D Analyses:

2-D Analyses:

PAVEMENT ANALYSIS: Soil-Structure Interaction Engineering


PAVEMENT PROFILE: A 2-D view of a 3-D Engineering Solution

LWPRWP


GPS3 Site 55-3009

-15

-10

-5

0

5

10

15

50 60 70 80 90 100Distance, m

Elevat

ion, m

m

LWPRWP

NOTES:1. Highest IRI of all GPS3 pavements less than 10 years old. 2. High faulting at an early age.3. Sandy clay subgrade (PI=14.5, w%=13), sand and gravel with 11% P200 base.4. Built in 1984, 300-350 KESAL/yr, 220 mm PCC, no dowels.Profile Date: 6/19/1992ProfileTime: 3:51:44 PM

10± mm

Profile Date: June 19, 1992Profile Time: 15:51:44

* “Thermally” Curved-Down at this time of day.* High Level of “Locked-In” Warp and Faulting.

Curved Way Up

R


Split Profile into 2 Sub-Matrices

X1 L1 R1X2 L2 R2X3 L3 R3. . .

. . .

Xn Ln Rn

= +

Raw ProfileDiscontinuities(cracks, joints...)

Continuous Slab Segments


0

0.005

0.01

0.015

0.02

0.025

340 345 350 355 360 365

Distance, feet

Elev

atio

n, fe

et

What is the Curvature of This?

GPS3 55-3009

“Structurally Continuous” WARPED SLAB

See TRB Paper# 092061: Measuring Curvature in Concrete Slabs and Connecting the Data to Slab Modeling Theory


0

0.005

0.01

0.015

0.02

0.025

340 345 350 355 360 365

Distance, feet

Elev

atio

n, fe

et

Slope = -0.00235

Slope = +0.00372

LzLz

L

dxxzL

mean)0(')(')(''

0 −== ∫κ

All Have Same Average CurvatureBut Different Statistics: std. deviation,

median, max., min…..

SINE-WAVE PERTUBATION


Average Curvature Over These Spans = Zero

Slope = ZeroSlope = Zero

Discontinuity

Ele

vatio

n

κAVG concept not valid through a working/hinging joint or crack


Discrete Slope

-0.04-0.03-0.02-0.01

00.01

0 15 30 45 60 75Distance, m

Slop

e, l/l

Discrete Curvature

-0.3-0.2-0.10.10.20.3

0 15 30 45 60 75Distance, m

Cur

vatu

re,

1/m

x10

00

Elevation

-15-10-505

1015

0 15 30 45 60 75Distance, m

Elev

atio

n,

mm

LWP

RWP

Upward Translation = “Rocking”

Moment Hinge

55-3009z = f(x)

dxdz

d zdx

2

2

See TRB Paper No. 06-0711For how to evaluate slab tilt and pumping from profile slope data


x

z R, Radius of Curvature1/κ =

CURVATURE of f(x) =

Second Derivative

κ ≈d zdx

2

2

1R


-0.0005

-0.0004

-0.0003

-0.0002

-0.0001

0

0.0001

0.0002

0.0003

0.0004

0.0005

3:00 AM 5:00 AM 7:00 AM 9:00 AM 11:00 AM 1:00 PM 3:00 PM 5:00 PM 7:00 PM 9:00 PM

Aver

age

Slab

Cur

vatu

re, 1

/ft

Time of Testing

Comparing to National Database 1-AC18(22)-a

1-AC18(22)-b

2-AC17-a

2-AC17-b

3-CT16

4-AC18-a

4-AC18-b

5-AGG18

6-CT16

7-AGG17

8-AGG15

9-AGG14

10-AGG14

11-CT14

LTPP GPS3 RWP

Howell I-96

Search “IPRF Joint Load Transfer” for Final Report describing airfield test sites shown

I-96 Site


-0.0005

-0.0004

-0.0003

-0.0002

-0.0001

0

0.0001

0.0002

0.0003

0.0004

0.0005


Aver

age

Slab

Cur

vatu

re, 1

/ft

Time of Testing


1-AC18(22)-b

2-AC17-a

2-AC17-b

3-CT16

4-AC18-a

4-AC18-b

5-AGG18

6-CT16

7-AGG17

8-AGG15

9-AGG14

10-AGG14

11-CT14

LTPP GPS3 RWP

Howell I-96

Trying to Measure Curl/Warp includes the difficult task of trying to measure or verify a “ZERO” value.


OK, Zero +/- How Much ????

How precise is your method?Precision mostly related to texture size


# of arcs = 20+22+24+26+28+30+32+34 Arc Values = 216 Arc Values from 18-ft Slab LWP

2 Wheel Paths = 432 arcs, 32 end slopes, 16 κ-stringsReport: Curvature Frequency Distribution

Number of ArcsStandard Deviation of Arc CurvaturesMedian, Avg, Max, Min CurvatureAverage Continuous Segment LengthFault Sizes.....many other indices

Arc lengths = 8’ 7’ 6’ 5’ 4’ 3’ 2’ 1’

For a single 18-ft slab we get:


The Central Limit Theorem- For any large population having finite standard deviation, the mean of sample size, n, approaches the mean of the population as n becomes large.

nκσStandard Error for Predicted Mean Curvature =


00.000010.000020.000030.000040.000050.000060.000070.000080.00009

0 5 10 15 20 25 30 35 40

Number of Slabs

Avg

. Cur

vatu

re S

td. E

rror

, ft-1

500-ft Sample

Single Slab

Standard error values are most related to the size of pavement surface texture and surface finishing/flaw features.

9,000-ft uniform section


Site: R10 Middle Lane, 5500-6000Profile Date: 10/23/15 Curvature SummaryProfileTime: 8:11 AM

Avg. hinge spacing = 11.9Curvature Index Value Sample Size StdDev Std Error of MeanLeave Slab Arcs 0.27 1228 2.41 0.069

Approach Slab Arcs 0.30 518 2.50 0.1106" Arcs 0.25 1380 2.43 0.06512" Arcs 0.29 1029 1.06 0.03318" Arcs 0.29 874 0.63 0.02124" Arcs 0.30 735 0.44 0.01630" Arcs 0.30 617 0.34 0.01436" Arcs 0.30 512 0.29 0.01342" Arcs 0.29 415 0.26 0.01348" Arcs 0.29 330 0.24 0.013

6" Spline Arcs 0.25 1380 0.65 0.01812" Spline Arcs 0.31 1031 0.42 0.01318" Spline Arcs 0.32 875 0.34 0.01224" Spline Arcs 0.31 735 0.29 0.01130" Spline Arcs 0.31 617 0.27 0.01136" Spline Arcs 0.29 512 0.26 0.01242" Spline Arcs 0.26 415 0.26 0.01348" Spline Arcs 0.30 330 0.22 0.012All Arc Average 0.28 7638 1.33 0.015

All Arc Mean 0.31 7638 1.33 0.015All Arc Median 0.33 7638 1.33 0.015Spline Average 0.29 5895 0.42 0.006

Spline Trim Mean 0.32 5895 0.42 0.006Spline Median 0.32 5895 0.42 0.006

Leave Slab Splines 0.30 1228 0.56 0.016Approach Slab Splines 0.26 518 0.64 0.028

Short Slab Index 0.33 3283 1.71 0.030Old Byrum CI (1999) 0.2816 5 0.0219 0.010Current Byrum CI 0.2872 15279 0.89 0.0072

Curvature analysis summary output table.

Software calculates the curvature statistics for the raw data arcs, and then does the same arc calculations on cubic splines fit at 2.5-ft intervals through the raw data. Standard error is reduced using a spline fitting technique.

0.0072/sqrt(18) = 0.0017 ?

Curvature Units = ft-1 x 1000


POB

POE

9,000-ft length “Uniformly Behaving Section”18 separate 500-ft analysis samples


R10 Middle Lane, 5500-6000 23-Oct-15 8:11:00

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

75 100 125 150 175 200 225 250

Elev

atio

n, in

.

Distance, ft.

ElevationLWP RWP

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

75 100 125 150 175 200 225 250

Slo

pe, i

n/ft

Faulted JointUn-Faulted Joint

Slope-of-slope in slabs ≅ 0.075/14(12) = 0.00045 ft-1Curved Slabs

texture


R2 Right Lane, 5000-5500 23-Oct-15 6:29:00

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

75 100 125 150 175 200 225 250

Elev

atio

n, in

.

Distance, ft.

ElevationLWP RWP

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

75 100 125 150 175 200 225 250

Slo

pe, i

n/ft

Faulted Joint, size ≅ 0.5(0.3)25.4 = 3.8 mm

Tilted Patches, approach-side uplift = 6’(0.05) = 0.30-inch (7.6 mm) uplift

Original curved slab segments

Pumping/tilted slabs

Mid-slab cracks


60

70

80

90

100

110

120

130

5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00

Avera

ge IR

I. in/

miEB I-96 Howell

0 500 10001500 2000 25003000 3500 40004500 5000 55006000 6500 70007500 8000 8500average 4th Order Fit to Average

22 profiles obtained 5AM to 1PMIRI trends per 500-ft segment

Uniform SegmentAverage Behavior


0

1

2

3

4

5

6

7

8

9

10

5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00

Avg.

Fault

/Hing

e Elev

ation

Diffe

rence

, mm

EB I-96 Howell


Average Fault Size


0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00

Med

ian W

heelp

ath Cu

rvatu

re (1/

ft x 10

00)

EB I-96 Howell


Approx. Locked-In Curvature (Warp) Values= zero-temperature-gradient-moment/bending

22 profiles obtained 5AM to 1PMSlab Curvature Index, CI


y = 157.32x + 70.74R² = 0.981

60

70

80

90

100

110

120

0 0.05 0.1 0.15 0.2 0.25

IRI,

in/m

i

Average Slab Curvature, 1/ft x 1000

Site Data

Site-Specific Curling vs. IRI trend: Sites with longer slabs would likely have steeper sloped trends


0

0.05

0.1

0.15

0.2

0.25

0.3

5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00

Med

ian W

heelp

ath C

urva

ture

, (1/ft

x 100

0)

Time of Day

EB I-96 East of Latson Road

Middle Lane 1-ft to 3-ft arc data

Middle Lane 1-ft to 8-ft arc data

Right Lane 1-ft to 3-ft arc data

30

35

40

45

50

55

60

5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00

Appr

ox. A

ir Tem

p. Ho

well,

MI

Air Temp.

Slab Curvature


0

0.05

0.1

0.15

0.2

0.25

0.3

0 to 500 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000 6500 7000 7500 8000 8500

Approx. Locked-in Warp Slab Curvature, 1/ft x 1000

0

20

40

60

80

100

120

140

0 to 500 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000 6500 7000 7500 8000 8500

IRI, in/mi

0

20

40

60

80

100

0 to 500 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000 6500 7000 7500 8000 8500

Sum of Fault Sizes, mm/500 ft

0

10

20

30

40

50

60

0 to 500 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000 6500 7000 7500 8000 8500

Slab Slope Index; Pumped Volume, cft/lane/mile

d zdx

2

2

dxdz

Discontinuities

Ride Quality Index

Slab Warp

Slab Tilting/Pumping

500-ft averages


Regression StatisticsMultiple R 0.94732273R Square 0.89742035Adjusted R Square 0.89583814Standard Error 4.15170914Observations 396

ANOVAdf SS MS F Significance F

Regression 6 58659.46989 9776.578 567.1958 6.9404E-189Residual 389 6705.071951 17.23669Total 395 65364.54184

Coefficients Standard Error t Stat P-valueIntercept 25.9744358 4.747270717 5.471446 8.01E-08CI_median 47.8168985 3.529127219 13.54921 1.57E-3412StdevCI 12.1703799 3.171571857 3.837334 0.00014536StdevCI 30.036206 3.719987784 8.074275 8.58E-15Avg Flt Size 5.593806 1.35289643 4.134689 4.36E-05#Faults 0.50723744 0.305084711 1.662612 0.097196ToTFlt, mm 0.82260559 0.244979056 3.357861 0.000863

60

70

80

90

100

110

120

130

140

60 70 80 90 100 110 120 130 140

Mea

sure

d IR

I, in

/mi

Predicted IRI, in/mi

500-ft samples IRI Prediction from profile shape parameters: simple linear regression

IRI breakdown data from a single uniformly behaving section


5060708090

100110120130140150

Warp Stdev Curv Faulting All

IRI,

in/m

i

I-96 Howell Regression Model

Site avg.

IRI breakdown data from a single uniformly behaving section


0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5Measured IRI, m/km

Pred

icte

d IR

I, m

/km

The LTPP GPS3 Profile DataAdjusted R2 = 0.93# Data Points = 902

IRI breakdown data from many different pavement sections from the LTPP GPS3


Sensitivity Analysis for the IRI Regression Model

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Faulting Avg. Slab Curvature Stdev Curvature All Parameters

IRI

, m/k

m

"Average" LTPP GPS3 Profile

High

Low

Very Curved

Flat

None

All High

All Low

HighHigh

LowFlat

Very Curved

None

High

“Avg.” GPS3 JPC

≅ 115 in/mi

IRI breakdown data from many different pavement sections -LTPP GPS3


Curling = “Average Slab Curvature Change” ≅ 0.00016 ft-1 change for a total change in air temperature of about 20 degrees Fahrenheit over a 5-hour period 8AM (min. temp) to 1PM (max. temp) for testing in October.

Warping = “Average Slab Curvature at/near Zero-Gradient Time” ≅ +0.00020 ft-1, with apparent locked-in warp curvatures in the 500-ft samples ranging between about +0.00026 and +0.00007 ft-1

Middle Lane IRI 85 to 115 in/mi average of about 100 in/mi (not failed at 21 yr)

Truck Lane IRI = 165 to 300 in/mi average of about 200 in/mi (near terminal at 21 yr)

IRI Change = 25 in/mi change for a slab curvature change (curling) of about 0.00016 ft-1

TEST SITE SUMMARY

LTPP GPS3 = 70 in/mi change for about 0.00050 ft-1 range in CI


-0.0005

-0.0004

-0.0003

-0.0002

-0.0001

0

0.0001

0.0002

0.0003

0.0004

0.0005


Aver

age

Slab

Cur

vatu

re, 1

/ft

Time of Testing


1-AC18(22)-b

2-AC17-a

2-AC17-b

3-CT16

4-AC18-a

4-AC18-b

5-AGG18

6-CT16

7-AGG17

8-AGG15

9-AGG14

10-AGG14

11-CT14

LTPP GPS3 RWP

Howell I-96

Slab Curvature Noticeable by Drivers at >≅ 0.00015 ft-1

Perception threshold

Perception threshold

i-96 case study: jointed concrete pavement curling and warp … byrum.pdf · 2020-04-17 · rwp. 30...

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